2 A special railway coach detects faults in the railway track before they become dangerous.
- Write down the conditions required for the numbers of faults in the track to be modelled by a Poisson distribution.
You should now assume that these conditions do apply, and that the mean number of faults in a 5 km length of track is 1.6 .
- Find the probability that there are at least 2 faults in a randomly chosen 5 km length of track.
- Find the probability that there are at most 10 faults in a randomly chosen 25 km length of track.
- On a particular day the coach is used to check 10 randomly chosen 1 km lengths of track. Find the probability that exactly 1 fault, in total, is found.